The least positive value of k, for which the quadratic equation 2x² + kx - 4 = 0 has rational roots, is (A) ± 2√(2) (B) 2 (C) ± 2 (D) √(2)

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 8

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQQuadratic Equations

The least positive value of k, for which the quadratic equation $2 x^{2} + k x - 4 = 0$ has rational roots, is

(A) $\pm 22$
(B)2
(C) $\pm 2$
(D) $2$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The nature of the roots depends on the discriminant $b^{2} - 4 a c$ .

Hint 2

Find a positive integer $k$ that makes $k^{2} + 32$ a perfect square.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

The roots are rational when the discriminant is a perfect square: $D = k^{2} - 4 (2) (- 4) = k^{2} + 32$ .
Test the options:
- $k = \pm 22$ gives $D = 40$ , not a perfect square.
- $k = 2$ gives $D = 34$ , not a perfect square.
- $\pm 2$ is not a single positive value.
- $k = 2$ gives $D = 36 = 6^{2}$ , a perfect square.
So the required least positive value is $k = 2$ (the roots are then $1$ and $- 2$ ). Option (B).
1 mark

Answer: k = 2, option (B)

Where the marks are

Requires $D = k^{2} + 32$ to be a perfect square and identifies $k = 2$ , option (B) (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Nature of Roots and Discriminant

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/1/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2023: question 8

Hints

Step-by-step solution

Revise the chapter

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